Wideband graphene-based electro-optic entangler

ABSTRACT

A electronic method, includes receiving, by a graphene structure, a SPP mode of a particular frequency. The electronic method includes receiving, by the graphene structure, a driving microwave voltage. The electronic method includes generating, by the graphene structure, an entanglement between optical and voltage fields.

BACKGROUND

Entanglement has been used in a variety of applications that includequantum teleportation, satellite quantum communication, submarinequantum communication, quantum internet, quantum error correction, andquantum cryptography. Various configurations exist that can initiateentanglement, including the use of a beam splitter, two trapped ionsentanglement, and entanglement of two microwave radiations. In theentanglement of microwave and optical fields, several systems exist buthave limitations. This includes a sensitivity of a mechanical resonatorto thermal noise. In other approaches, a whispering gallery moderesonator filled with electro-optical material may be used. In thisapproach, an optical field is coupled to the whispering galleryresonator while a microwave field drives the resonator. However, thereare limitations that include that the free spectral range of thewhispering resonator must match the microwave frequency which can alsolimit tunability. Thus, there is no effective technique that achieve awide band entanglement of microwave and optical fields with a largetunability

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram of an example model graphene structural design;

FIG. 2 is a diagram of an example model capacitance design;

FIGS. 3 and 4 are example electronically generated graphs;

FIGS. 5 and 6 are example electronically generated graphs;

FIG. 7 is an example electronically generated graph;

FIG. 8 is an example electronically generated graph;

FIGS. 9 and 10 are example electronically generated graphs;

FIG. 11 is an example computer device;

FIG. 12 is an example system; and

FIG. 13 is an example system

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The following detailed description refers to the accompanying drawings.The same reference numbers in different drawings may identify the sameor similar elements.

Systems, devices, and/or methods described herein may provide formicrowave and optical entanglement using a capacitor loaded withgraphene plasmonic waveguide. In embodiments, a quantum microwave signalof a particular frequency may drive a capacitor (e.g., an electricalcapacitor) while an optical field (e.g., an optical pump) of aparticular frequency is launched to the graphene waveguide in a surfaceplasmon polariton (i.e., SPP) mode. In embodiments, the two fields(microwave and optical) may interact based on electrically modulating agraphene optical conductivity. As such, upper and lower SPP sidebandmodes (e.g., ω₂=ω₁+ω_(m) and ω₃=ω₁−ω_(m)) are generated. In embodiments,the microwave signal and the lower SPP sideband are entangled based on aparticular pump intensity.

As such, a quantum mechanics model may be generated to determine fieldsevolution. In embodiments, the entanglement of the microwave and opticalfields may be evaluated based on waveguide length, pump intensity, andmicrowave frequency. In embodiments, the two fields (microwave andoptical) may be entangled over a vast microwave frequency range.Additionally, a quantity of entangled photons are also generated at thelower SPP sideband. Thus, the systems and methods described hereinprovides a tunable mechanism for microwave-optical entanglement within amore efficient quantum system.

Accordingly, microwave and optical fields entanglement may be providedbased on electrical capacitor loaded with graphene plasmonic waveguide.In embodiments, the microwave signal may drive parallel plates of thecapacitor, with the graphene waveguide supporting a surface plasmonpolariton (i.e., SPP) mode. The microwave voltage and the SPP modeinteract via electrically modifying the graphene optical conductivity.In embodiments, a driving microwave signal and a lower sideband areentangled for a particular pump intensity |A₁|². In embodiments, theentanglement may be analyzed and changed based on different parametersincluding the graphene waveguide length, the microwave frequency, themicrowave number of photons and the pump intensity. Thus, entanglementoccurs, and can be tunable, over a larger frequency range based onparticular pump intensities.

FIG. 1 shows an example superconducting parallel plate capacitor loadedwith a graphene layer. In embodiments, two plates (each 102) areseparated by a distance d and have a particular area (L×W). Inembodiments, a graphene layer is located equidistant between the twoplates. In alternate embodiments, the graphene layer may be closer toone plate than the other plate. In embodiments, the capacitance may beC=εε₀/d. In embodiments, the capacitance may be driven by a microwavesignal as described by equation (1):

V _(m) =V _(e) ^(−iωm t) +c.c.   (1)

In embodiments, a transverse magnetic (i.e., TM) surface plasmonpolariton (SPP) mode is coupled to the graphene waveguide. Inembodiments, the SPP mode is described by its associated electrical (andmagnetic) fields, given by equations (2) and (3):

{right arrow over (E)}=

(z)(

_(x)(x){tilde over (e)}_(x)+

_(z)(x){tilde over (e)} _(z))^(−i(ωt−βz)) +c.c   (2)

{right arrow over (H)}=

(z)

_(y)(x){right arrow over (e)} _(y) e ^(−i(ωt−βz)) +c.c   (3)

In embodiments, U(z) is a complex amplitude, D_(x)(x)={(βi/ωεε0)e^(αx)for x<0; (βi/ωεε0)e^(−αx) for x>0}, D_(z)(x)={(αi/ωεε0)e^(αx) for x<0;(αi/ωεε0)e^(−αx) for x>0}, and D_(y)(x)={e^(αx) for x<0; e^(−αx) forx>0} are special distributions of the SPP mode, α=(β²−εk²)^(1/2) andk₀=ω/c are the free space propagation constant, and c is the speed ofthe light in the vacuum. In embodiments, a dispersion relation of theSPP mode is given by equation (4):

β=k ₀(1−(2/Z ₀σ_(s))²)^(1/2)   (4)

In embodiments, Z₀=377Ω is a free space impedance and σ_(s) is thegraphene conductivity. In embodiments, for an input SPP mode offrequency ω₁ and a driving microwave voltage of frequency Wm, an upperand lower SPP sidebands are generated at frequencies ω₂=ω₁+ω_(m) andω₃=ω₁−ω_(m) based on graphene conductivity modulation. In embodiments,associated electric fields with these particular SPP modes are given by

{right arrow over (E)} _(j)=

_(j)(z)(

_(xj)(x){right arrow over (e)} _(x)+

_(zj)(x){right arrow over (e)} _(z))e ^(−i(ω) ^(j) ^(t−β) ^(j) ^(z))+c.c

In embodiments, j includes {1,2,3}. In embodiments, upon implementing aperturbation approach, the effective propagation constant of the SPPmodes can be approximated by βj=β′_(j)+Vβ″e^(−iω) _(m) ^(t)+c.c, andthus, the corresponding effective permittivity of the SPP modes is givenby equation (5):

$\begin{matrix}{{\varepsilon_{{eff}_{j}} = {\varepsilon_{{eff}_{j}}^{\prime} = {{{+ {\mathcal{V}\varepsilon}_{{eff}_{j}}^{''}}e^{{- i}\omega_{m}t}} + {c.c.{where}}}}}{{\varepsilon_{{eff}_{j}}^{\prime} = {{\left( \frac{\beta_{j}^{\prime}}{k_{0_{j}}} \right)^{2}.\varepsilon_{{eff}_{j}}^{''}} = {2\frac{\beta_{j}^{\prime}\beta_{j}^{''}}{k_{0_{i}}^{2}}}}},\beta_{j}^{\prime}}} & (5)\end{matrix}$

is a solution of the dispersion related to equation (4), and

${\beta_{j}^{''} = {\frac{\beta_{j}^{\prime}}{1 - \left( {\frac{1}{2}Z_{0}\sigma_{s_{j}}^{\prime}} \right)^{2}}\frac{\sigma_{s_{j}}^{''}}{\sigma_{s_{j}}^{\prime}}}},{{and}\sigma_{s_{j}}^{''}}$

is the perturbed graphene conductivity term. In embodiments, the SPPmodes are contained between two plates with negligible overlapping withthe electrodes. In embodiments, the negligible overlapping can beachieved by separating the distance between two electrodes d larger than1/α. For example, if d=10/α, then 99.99% of the SPP mode is containedwithin the gap between two parallel plates.

In embodiments, interacting fields can be quantized by the followingrelations in equation (6):

$\begin{matrix}{{\mathcal{U}_{j} = {\frac{\left( {\hslash\omega}_{j} \right)^{\frac{1}{2}}}{{\xi_{j}^{\frac{1}{2}}\left( {\varepsilon_{0}\varepsilon_{{eff}_{i}}^{\prime}V_{L}} \right)}^{\frac{1}{2}}}{\hat{a}}_{j}}},{{{and}\mathcal{V}} = {\left( \frac{2{\hslash\omega}_{m}}{C\mathcal{A}_{r}} \right)^{\frac{1}{2}}\hat{b}}}} & (6)\end{matrix}$

Where

-   -   â_(j) and {circumflex over (b)}are annihilation operators of the        j^(th) optical and microwave fields, respectively. In        embodiments, the SPP volume is:

V _(L)=

_(r)∫_(−∞) ^(+∞)(|

_(xj)|²+|

_(zj)|²)∂x

and a unit-less parameter is:

$\xi_{j} = {\frac{1}{2} + {\frac{\mu_{0}}{2\varepsilon_{0}\varepsilon_{{eff}_{j}}^{\prime}}\frac{\int_{- \infty}^{+ \infty}{{❘\mathcal{D}_{y_{j}}❘}^{2}{\partial x}}}{\int_{- \infty}^{+ \infty}{\left( {{❘\mathcal{D}_{x_{j}}❘}^{2} + {❘D_{z_{j}}❘}^{2}} \right){\partial x}}}}}$

which is introduced to match the expression of the free Hamiltonian ofthe SPP modes to the expression of the free Hamiltonian of thecorresponding unguided fields. Accordingly, the spatial distribution ofthe SPP modes is completely included in the conversion rates g₂ and g₃.In embodiments, the quantum Hamiltonian is given by equation (7):

=

₀+

₁   (7)

where equation (8) is:

$\begin{matrix}{{{\hat{\mathcal{H}}}_{0} = {{{\hslash\omega}_{m}{\hat{b}}^{\dagger}\hat{b}} + {\sum\limits_{j = 1}^{3}{{\hslash\omega}_{j}{\hat{a}}_{j}^{\dagger}{\hat{a}}_{j}}}}},{{{and}{\hat{\mathcal{H}}}_{1}} = {{\hslash g_{2}{\hat{a}}_{2}^{\dagger}\hat{b}{\hat{a}}_{1}} + {\hslash g_{3}{\hat{a}}_{1}^{\dagger}\hat{b}{\hat{a}}_{3}} + {h.c.}}}} & (8)\end{matrix}$

with h.c. is the Hermitian conjugate, and g₂ and g₃ are the conversionrates given by equations (9) and (10):

$\begin{matrix}{g_{2} = {\frac{1}{2}\varepsilon_{{eff}_{2}}^{''}\sin{c\left( {\frac{\beta_{1} - \beta_{2}}{2}L} \right)}{e^{i\frac{\beta_{1} - \beta_{2}}{2}L}\left( \frac{2\omega_{1}\omega_{2}{\hslash\omega}_{m}}{C\mathcal{A}_{r}\varepsilon_{{eff}_{1}}^{\prime}\varepsilon_{{eff}_{2}}^{\prime}} \right)}^{\frac{1}{2}}\frac{I_{12}}{\sqrt{\xi_{1}\xi_{2}}}}} & (9)\end{matrix}$ $\begin{matrix}{g_{3} = {\frac{1}{2}\varepsilon_{{eff}_{3}}^{''}\sin{c\left( {\frac{\beta_{3} - \beta_{1}}{2}L} \right)}{e^{i\frac{\beta_{3} - \beta_{1}}{2}L}\left( \frac{2\omega_{3}\omega_{1}{\hslash\omega}_{m}}{C\mathcal{A}_{r}\varepsilon_{{eff}_{1}}^{\prime}\varepsilon_{{eff}_{3}}^{\prime}} \right)}^{\frac{1}{2}}\frac{I_{13}}{\sqrt{\xi_{1}\xi_{3}}}}} & (10)\end{matrix}$ where$I_{mn} = \frac{\int_{- \infty}^{+ \infty}{\left( {{\mathcal{D}_{x_{m}}^{*}\mathcal{D}_{x_{n}}} + {\mathcal{D}_{z_{m}}^{*}\mathcal{D}_{z_{n}}}} \right){\partial x}}}{\sqrt{\int_{- \infty}^{+ \infty}{\left( {{❘\mathcal{D}_{x_{m}}❘}^{2} + {❘\mathcal{D}_{z_{m}}❘}^{2}} \right){\partial x}}}\sqrt{\int_{- \infty}^{+ \infty}{\left( {{❘\mathcal{D}_{x_{n}}❘}^{2} + {❘\mathcal{D}_{z_{n}}❘}^{2}} \right){\partial x}}}}$

In embodiments, the SPP pump at frequency ω₁ is intensive and treatedclassically. Thus, substituting a quantum Hamiltonian expression ofequation (7) into Heisenberg equations of motion, that is:

$\frac{\partial\hat{x}}{\partial t} = {\frac{i}{\hslash}\left\lbrack {\hat{\mathcal{H}},\hat{x}} \right\rbrack}$

and using the rotation approximation:

ô _(j) =Ô _(j) e ^(−iω) ^(|) ^(t)

the following equations of motions (equations (11), (12), and (13)) aregenerated:

$\begin{matrix}{{\frac{\partial{\hat{A}}_{2}}{\partial t} = {{{- \frac{\Gamma_{2}}{2}}{\hat{A}}_{2}} + {g_{2}A\hat{B}} + {\sqrt{\Gamma_{2}}{\hat{N}}_{2}}}},} & (11)\end{matrix}$ $\begin{matrix}{\frac{\partial{\hat{A}}_{3}}{\partial t} = {{{- \frac{\Gamma_{3}}{2}}{\hat{A}}_{3}} + {g_{3}A{\hat{B}}^{\dagger}} + {\sqrt{\Gamma_{3}}{\hat{N}}_{3}}}} & (12)\end{matrix}$ $\begin{matrix}{\frac{\partial\hat{B}}{\partial t} = {{{- \frac{\Gamma_{m}}{2}}\hat{B}} - {g_{2}A^{*}{\hat{A}}_{2}} + {g_{3}A{\hat{A}}_{3}^{\dagger}} + {\sqrt{\Gamma_{m}}{\hat{N}}_{m}}}} & (13)\end{matrix}$

In embodiments, the optical delay coefficient is given by:

Γ_(j)=2v _(g) Im(β′)

and the Γm represents microwave decay coefficient. In embodiments, thegroup velocity is:

$v_{g} = \frac{\partial f}{\partial\beta}$

In embodiments, the pump field amplitude Ai is considered with Π/2 phase(i.e., A₁=Ae^(iΠ/2)=iA), and N₂ and N_(m) are quantum Langevin noiseoperators. In embodiments, the dissipation is characterized by the timedecay rates, included in equations (11) and (13). Thus, based on afluctuation —dissipation theorem, the Langevin forces are included. Inembodiments, the quantum coupled equations of motion presented abovedescribe an evolution of the SPP modes and the driving microwave signal.

In embodiments, no steady state is considered as the interaction iscarried out while the propagating SPP modes are coupled to the opticalpump. Thus, the time rates of the SPP averages are non-zero, where:

$\left( {\frac{\partial\left\langle {\hat{A}}_{j} \right\rangle}{\partial t} \neq 0} \right)$

To evaluate the entanglement while fulfilling the non-zero requirement,the entanglement between the following factors is evaluated using theDuan's criterion in (14):

-   -   {circumflex over (B)} and Â₃        In embodiments, equation (14) is as follows:

$\begin{matrix}{\Lambda = {❘\begin{matrix}I & \left\langle {\hat{A}}_{3} \right\rangle & \left\langle {\hat{B}}^{\dagger} \right\rangle \\\left\langle {\hat{A}}_{3}^{\dagger} \right\rangle & \left\langle {{\hat{A}}_{3}^{\dagger}{\hat{A}}_{3}} \right\rangle & \left\langle {{\hat{A}}_{3}^{\dagger}{\hat{B}}^{\dagger}} \right\rangle \\\left\langle \hat{B} \right\rangle & \left\langle {{\hat{A}}_{3}\hat{B}} \right\rangle & \left\langle {{\hat{B}}^{\dagger}\hat{B}} \right\rangle\end{matrix}❘}} & (14)\end{matrix}$

and that entanglement exists whenever the determinant is negative (∧<0).In embodiments, average rate equations (equations (15), (16), and (17))are obtained by using equations (11), (12), and (13):

$\begin{matrix}{\frac{\partial\left\langle {\hat{A}}_{2} \right\rangle}{\partial t} = {{{- \frac{\Gamma_{2}}{2}}\left\langle {\hat{A}}_{2} \right\rangle} + {g_{2}A\left\langle \hat{B} \right\rangle}}} & (15)\end{matrix}$

$\begin{matrix}{\frac{\partial\left\langle {\hat{A}}_{3} \right\rangle}{\partial t} = {{{- \frac{\Gamma_{3}}{2}}\left\langle {\hat{A}}_{3} \right\rangle} + {g_{3}A\left\langle {\hat{B}}^{\dagger} \right\rangle}}} & (16)\end{matrix}$ $\begin{matrix}{\frac{\partial\left\langle \hat{B} \right\rangle}{\partial t} = {{{- \frac{\Gamma_{m}}{2}}\left\langle \hat{B} \right\rangle} - {g_{2}A^{*}\left\langle {\hat{A}}_{2} \right\rangle} + {g_{3}A\left\langle {\hat{A}}_{3}^{\dagger} \right\rangle}}} & (17)\end{matrix}$

Next, the regression method is used to model the rate equations of thefollowing averages:

-   -   Â₃ ^(†)Â₃        ,        Â₃ ^(†){circumflex over (B)}^(†)        ,        Â₃{circumflex over (B)}        and        {circumflex over (B)}^(†){circumflex over (B)}

In embodiments, equations (15), (16), and (17) are solved to obtainvalues to evaluate a condition in equation (14) at specific timeinterval t=L/v_(g). In embodiments, microwave and optical operators areconsidered uncorrelated at t=0, and thus:

Â _(j) ^(†) {circumflex over (B)} ^(†)

|_(t=0)=

Â _(j) {circumflex over (B)}

|_(t=0)=

In embodiments, the number of microwave photons at t=0, are as follows:

Â ₃ ^(†) Â ₃

|_(t=0)=0

Â ₂ ^(†) Â ₂

|_(t=0)=0

{circumflex over (B)} ^(†) {circumflex over (B)}

| _(t=0)

Based on the preceding examples and equations, an electrical capacitoris considered with air filling material. In embodiments, a graphenedoping concentration is n₀=10¹⁸ m⁻³, the pump frequency is ω₁/2Π=193 THzand the temperature is T=3 mK. In embodiments, the SPP propagationconstant β (and the decay time constant Γ are shown in FIG. 2 as arelationship to optical frequency. As such, by calculating a from thevalues of β, it is shown that for a separating distance of d=1 μm (whereC=8.85 μF/m²), the SPP field amplitude is identical to zero at theelectrodes location x, is

$x = {{\pm \frac{d}{2}}\left( {{{i.e}\ldots e^{{- \alpha}\frac{d}{2}}} = e^{- 34}} \right)}$

In embodiments, width W=1 μm and the length L is considered withdifferent values. As shown in FIG. 3 , the entanglement condition ∧ isevaluated versus the waveguide length. In embodiments, the optical pumpintensity is |A₁|²=10⁶, the microwave number of photons is

{circumflex over (B)} ^(†) {circumflex over (B)}| _(t=0)=10⁴

And, the three different microwave frequencies (ω_(m)/2Π) are considered−5 GHz, 15 GHz, and 45 GHz. Thus, the fields are entangled for differentwaveguide lengths. In embodiments, the entanglement is stronger for alarger microwave frequency. In embodiments, the entanglement strengthincreases against the waveguide length until losses begin to take over.In FIG. 4 , a number of generated photons at the lower sideband iscalculated. In embodiments, as shown in FIG. 4 , a greater number ofphotons are generated for an optimum waveguide length. In embodiments,with limited losses, both the entanglement and the number of photos atthe lower sideband have the same optimum waveguide length (L=2.7 μm).

FIGS. 5 and 6 shows a relationship between an entanglement conditionversus an optimum waveguide length (L=2.7 μm). In embodiments, differentmicrowave frequencies are analyzed. In FIG. 5 , ω_(m)/2Π with values at5 GHz, 15 GHz, and 20 GHz are considered. In FIG. 6 , ω_(m)/2Π withvalues at 60 GHz, 80 GHz, and 90 GHz. In both FIGS. 5 and 6 , theentanglement depends on pump intensity. In FIG. 5 , the entanglement isstronger for larger pump intensities.

In FIG. 6 , the entanglement is maximized over pump intensities and getsweaker for larger pump intensities. For example at ω_(m)/2Π=5 GHz, theentanglement is stronger for larger pump intensities. For ω_(m)/2Π=90GHz, reaches it maximum at |A₁|²=1.8×10⁷. In embodiments, theentanglement gets weaker for larger intensities and disappears forintensities greater than |A₁|²=2.5×10⁷.

In FIG. 7 , the example entanglement condition A and the number ofgenerated photons at the lower sideband are evaluated versus themicrowave number of photons. In embodiments, the entanglement isstronger for larger number of microwave photons. In embodiments, theentanglement is also stronger for the number of photons generated at thelower sideband. In embodiments, different microwave frequencies areconsidered. Thus, the entanglement strength and the number of generatedphotons become intensified for higher microwave frequencies. In FIG. 8 ,the number of optical photons at ω₃ versus the microwave number ofphotons is determined with |A₁|²=10⁶ and L=2.7 μm.

In FIGS. 9 and 10 , the entanglement condition A is analyzed againstmicrowave frequency. In embodiments, different pump intensities areconsidered. In FIG. 9 , the entanglement is considered for values of|A₁|² at 9×10⁶, 10.9×10⁶, and 12.9×10⁶. In FIG. 10 , the pumpintensities are considered for values of |A₁|² at 1.9×10⁷, 2.1×10⁷, and2.4×10⁷. In embodiments, as shown in FIG. 9 , the entanglement isstronger for higher microwave frequency and larger pump intensity. Inembodiments, as shown in FIG. 10 , the entanglement strength increasesagainst microwave frequency until reaching an optimal value and thenstarts to decrease until there is no entanglement. In embodiments, boththe optimum frequency and the frequency at which disentanglement isreached are for smaller for a larger pump intensity. However, a largepump intensity may result in stronger entanglement.

For example, for |A₁|²=1.9 ×10⁷, the entanglement strength is maximal atthe optimum microwave frequency ω_(m)/2Π=86 GHz and disentanglement isreached at ω_(m)/2Π=100 GHz. However, for |A₁|²=2.4×10⁷, theentanglement optimum frequency is ω_(m)/2Π=76 GHz and disentanglement isreached at ω_(m)/2Π=96 GHz. In these non-limiting examples, theentanglement at ω_(m)/2Π=76 for |A₁|²=2.4×10⁷ is stronger than that atω_(m)/2Π=86 for |A₁|²=1.9×10⁷.

Based on the above example formulas and charts, microwave and opticalfields entanglement based on electrical capacitor loaded with grapheneplasmonic waveguide are analyzed for optimal values. In embodiments, amicrowave voltage is applied to the capacitor while a graphene waveguideis subjected to an optical surface plasmon polariton (i.e., SPP) input.Accordingly, SPP sidebands are generated at the expense of the input SPPpump and the driving microwave signal. In embodiments, a quantummechanics model is generated to describe the fields interactions andderived motion equations indicates entanglement between the microwaveand the lower SPP sideband.

In embodiments, Duan's criterion is used to investigate theentanglement. In embodiments, the equations needed to evaluate theDuan's determinant are derived from the motion equation using thequantum regression theorem. Thus, the microwave signal and the lower SPPsideband are entangled over a vast microwave frequency. In embodiments,the entanglement is evaluated against the waveguide length. Limited bylosses, it is observed that an optimum waveguide length at which theentanglement strength (and number of photons at the lower side band) ismaximized. Additionally, the entanglement versus the SPP pump intensitytakes into account an optimum length. In embodiments, the entanglementis stronger for larger pump intensity. However, for intensive pumpinputs and microwave frequencies greater than 50 GHz, there is anoptimum pump intensity at which the entanglement is maximized and thendecreases for larger intensity values until disentanglement is observed.In embodiments, the entanglement is evaluated versus the microwavenumber of photons. The larger the number of microwave photons, thestronger the entanglement. In addition, the entanglement is evaluatedversus the microwave frequency. It is found that the entanglement isattained over a particular range with a particular pump intensity. Thus,a frequency tunable process is provided for effective microwave-optimalentanglement.

FIG. 11 is a diagram of example components of a device 1100. Device 1100may correspond to a computing device, such as devices 1100, 1200, 1300and/or 1302. Alternatively, or additionally, devices 1100, 1200, 1300,and/or 1202 may include one or more devices 1100 and/or one or morecomponents of device 1100.

As shown in FIG. 11 , device 1100 may include a bus 1110, a processor1120, a memory 1130, an input component 1140, an output component 1150,and a communications interface 1160. In other implementations, device1100 may contain fewer components, additional components, differentcomponents, or differently arranged components than depicted in FIG. 11. Additionally, or alternatively, one or more components of device 1100may perform one or more tasks described as being performed by one ormore other components of device 1100.

Bus 1110 may include a path that permits communications among thecomponents of device 1100. Processor 1120 may include one or moreprocessors, microprocessors, or processing logic (e.g., a fieldprogrammable gate array (FPGA) or an application specific integratedcircuit (ASIC)) that interprets and executes instructions. Memory 1130may include any type of dynamic storage device that stores informationand instructions, for execution by processor 1120, and/or any type ofnon-volatile storage device that stores information for use by processor1120. Input component 1140 may include a mechanism that permits a userto input information to device 1100, such as a keyboard, a keypad, abutton, a switch, voice command, etc. Output component 1150 may includea mechanism that outputs information to the user, such as a display, aspeaker, one or more light emitting diodes (LEDs), etc.

Communications interface 1160 may include any transceiver-like mechanismthat enables device 1100 to communicate with other devices and/orsystems. For example, communications interface 1160 may include anEthernet interface, an optical interface, a coaxial interface, awireless interface, or the like.

In another implementation, communications interface 1160 may include,for example, a transmitter that may convert baseband signals fromprocessor 1120 to radio frequency (RF) signals and/or a receiver thatmay convert RF signals to baseband signals. Alternatively,communications interface 1160 may include a transceiver to performfunctions of both a transmitter and a receiver of wirelesscommunications (e.g., radio frequency, infrared, visual optics, etc.),wired communications (e.g., conductive wire, twisted pair cable, coaxialcable, transmission line, fiber optic cable, waveguide, etc.), or acombination of wireless and wired communications.

Communications interface 1160 may connect to an antenna assembly (notshown in FIG. 11 ) for transmission and/or reception of the RF signals.The antenna assembly may include one or more antennas to transmit and/orreceive RF signals over the air. The antenna assembly may, for example,receive RF signals from communications interface 1160 and transmit theRF signals over the air, and receive RF signals over the air and providethe RF signals to communications interface 1160. In one implementation,for example, communications interface 1160 may communicate with anetwork (e.g., a wireless network, wired network, Internet, etc.).

As will be described in detail below, device 1100 may perform certainoperations. Device 1000 may perform these operations in response toprocessor 1120 executing software instructions (e.g., computerprogram(s)) contained in a computer-readable medium, such as memory1130, a secondary storage device (e.g., hard disk, CD-ROM, etc.), orother forms of RAM or ROM. A computer-readable medium may be defined asa non-transitory memory device. A memory device may include space withina single physical memory device or spread across multiple physicalmemory devices. The software instructions may be read into memory 1030from another computer-readable medium or from another device. Thesoftware instructions contained in memory 1130 may cause processor 1120to perform processes described herein. Alternatively, hardwiredcircuitry may be used in place of or in combination with softwareinstructions to implement processes described herein. Thus,implementations described herein are not limited to any specificcombination of hardware circuitry and software.

FIG. 12 is an example diagram. FIG. 12 describes device 1200,communication 1202, and communication 1204. In embodiments, device 1200may a computing device with features/structures similar to thatdescribed in FIG. 12 . In embodiments, device 1200 may be a computingdevice that is part of a laptop, desktop, tablet, smartphone, and/or anyother device that may receive communication 1202, analyze communication1202, and generate output 1204 based on communication 1202. As shown inFIG. 12 , communication 1202 may be received by device 1200 (e.g., viakeyboard inputs, touchscreen inputs, voice inputs, etc.). Inembodiments, communication 1202 may include information about a graphenestructure, such as number of layers, thickness, distance between layers,electric features, dielectric features, etc. In embodiments, device 1200may receive communication 1202 and, based on one or more of equations(1) to (17), as described above, that generate output 1204 that includesinformation about entanglement of microwave and optical fields with aparticular waveguide length, frequency, and/or other informationassociated with equations (1) to (17).

FIG. 13 is an example diagram. FIG. 13 describes device 1300, device1302, input 1304, and output 1206. In embodiments, device 1200 may acomputing device with features/structures similar to that described inFIG. 13 . In embodiments, device 1300 may be a computing device that ispart of a laptop, desktop, tablet, smartphone, and/or any other devicethat may receive communication 1302, analyze communication 1304, andgenerate output 1306 based on communication 1304. In embodiments, device1300 may be a computing device that is part of a laptop, desktop,tablet, smartphone, and/or any other device that may receivecommunication 1204, analyze communication 1304, and generate output 1306based on communication 1304. In embodiments, device 1302 may be acomputing device that is part of a laptop, desktop, tablet, smartphone,and/or any other device that may receive output 1306, analyze output1306, and generate output 1308 based on output 1306.

In embodiments, communication 1304 may include microwave fieldinformation based on one or more of equations (1) to (17) as describedabove. In embodiments, device 1300 may receive communication 1304 andanalyze communication 1304 based on one or more equations (1) to (17).In embodiments, device 1200 may generate output 1306. In embodiments,output 1306 may include electronic design information for a graphenestructure. In embodiments, output 1206 may be received by device 1302.In embodiments, device 1302 may generate a physical graphene structure(e.g., graphene structure 100). In embodiments, device 1302 may includewafer fabrication systems. In embodiments, device 1302 may generate agraphene structure or a composite structure that includes a graphenestructure.

Even though particular combinations of features are recited in theclaims and/or disclosed in the specification, these combinations are notintended to limit the disclosure of the possible implementations. Infact, many of these features may be combined in ways not specificallyrecited in the claims and/or disclosed in the specification. Althougheach dependent claim listed below may directly depend on only one otherclaim, the disclosure of the possible implementations includes eachdependent claim in combination with every other claim in the claim set.

While various actions are described as selecting, displaying,transferring, sending, receiving, generating, notifying, and storing, itwill be understood that these example actions are occurring within anelectronic computing and/or electronic networking environment and mayrequire one or more computing devices, as described in FIG. 11 , tocomplete such actions. Furthermore, it will be understood that thesevarious actions can be performed by using a touch screen on a computingdevice (e.g., touching an icon, swiping a bar or icon), using akeyboard, a mouse, or any other process for electronically selecting anoption displayed on a display screen to electronically communicate withother computing devices. Also it will be understood that any of thevarious actions can result in any type of electronic information to bedisplayed in real-time and/or simultaneously on multiple user devices.For FIGS. 2 to 9 , the electronic graphs may be generated by a computingdevice, such as device 1000, and displayed via a graphical user device(GUI).

No element, act, or instruction used in the present application shouldbe construed as critical or essential unless explicitly described assuch. Also, as used herein, the article “a” is intended to include oneor more items and may be used interchangeably with “one or more.” Whereonly one item is intended, the term “one” or similar language is used.Further, the phrase “based on” is intended to mean “based, at least inpart, on” unless explicitly stated otherwise. Also, the phrase“converted text,” or “converted information” may indicate informationthat has been converted from handwritten or non-handwritten informationto printed information. The phrase “information” may indicate letters,words, numbers, and/or symbols. The phrase “text” may indicate letters,numbers, and/or symbols. The phrases “information” and “text” mayindicate the same thing, i.e., letters, numbers, and/or symbols. Also,while the above examples are associated with prescriptions, pharmacists,and doctors, the above example actions may also be used for otherscenarios and analysis of other types of handwritten text, such as withpurchase orders, shipping orders, etc.

In the preceding specification, various preferred embodiments have beendescribed with reference to the accompanying drawings. It will, however,be evident that various modifications and changes may be made thereto,and additional embodiments may be implemented, without departing fromthe broader scope of the invention as set forth in the claims thatfollow. The specification and drawings are accordingly to be regarded inan illustrative rather than restrictive sense.

What is claimed is:
 1. A graphene structure, comprising: a graphenelayer, wherein: the graphene layer is between two plates, and a surfaceplasmon polariton (SPP) mode is generated and is 99.99% within a gapbetween the two plates.
 2. The graphene structure of claim 1, whereinthe graphene layer is of a particular length.
 3. The graphene structureof claim 1, wherein the graphene structure generates an entanglement ofoptical and voltage fields.
 4. The graphene structure of claim 1,wherein the graphene structure requires a driving microwave voltage thatis less than 10 microvolts.
 5. The graphene structure of claim 1,wherein the graphene structure receives the SPP mode at a particularfrequency.
 6. The graphene structure of claim 1, wherein the graphenestructure is pumped by an optical pump.
 7. The graphene structure ofclaim 5, wherein, based on the SPP mode, an upper and lower SPP sidebandare each generated at particular frequencies.
 8. The graphene structureof claim 7, wherein a microwave signal and the lower SPP sideband areentangled based on a particular pump intensity.
 9. The graphenestructure of claim 1, wherein the graphene structure provides a tunablemechanism for microwave-optical entanglement.
 10. The graphene structureof claim 3, wherein the entanglement is changed based on at least oneof: graphene waveguide length, microwave frequency, microwave number ofphotons, and pump intensity.
 11. The graphene structure of claim 1,wherein a microwave signal and a lower SPP sideband associated with thegraphene structure, are entangled over a microwave frequency, whereinthe entanglement is evaluated against a waveguide length.
 12. Thegraphene structure of claim 11, wherein the entanglement versus the SPPpump intensity is based on optimum length, wherein the entanglement isstronger for larger pump intensity.
 13. The graphene structure of claim11, wherein the entanglement is evaluated versus microwave number ofphotons, wherein the larger the number of microwave photons, thestronger the entanglement.